It is well known that a stable matching in smi can be found in \(O(m)\)  time via the Gale-Shapley algorithm [1]}, where \(m\)  is the total length of all agents preference lists. This algorithm requires either men or women to be the proposers and those of the opposite gender are receivers. However, this procedure naturally produces a proposer-optimal stable matching where members of the proposer group will be assigned to their best possible partner in any stable matching. Unfortunately, this also ensures a receiver-pessimal stable matching in which members of the receiver group will be assigned their worst assignees in any stable matching.
